Local Energy Decay for Linear Wave Equations with Localized Dissipation

Abstract

A local energy decay result can be derived for a linear wave equation in an exterior domain Ω ⊂ R^N, which has a localized dissipation being effective only near a part of the boundary ∂Ω. In this case we do not assume any compactness of the support on the initial data differently from the usual well-known case. Our result generalizes some previous results due to Morawetz [9], Nakao [12], Ikehata [4] and Ikehata-Nishihara [6].